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Coherence between electronic states occurs when at least two time-evolving eigenstates form a superposition state by linear combination and the frequencies of the two states feature a constant phase difference. The simplest representation is the coherence between two eigenstates although in principle an infinite number of states may be in coherent superposition. However, an event known as dephasing occurs when other eigenstates without constant phase differences to the superposition state interfere with the coherent superposition causing the coherent states to fall out of phase with one another. The length of time a superposition state remains in coherence before dephasing is referred to as the “coherence lifetime.”

Long coherence lifetimes in molecular systems are uncommon. However, bimetallic Pt(II) complexes show signatures of exhibiting such long-lived coherences in experiment making them attractive systems for probing this phenomenon. Even more attractive is the distinct dominance of two excited charge transfer (CT) excited states in coherent superposition upon excitation. This enables modeling these systems with a simple three-state (two coherent states and a “bath” state) time-dependent model. Furthermore, these complexes may feature tunable parameters such as Pt—Pt bond distance capable of modulating the coherence lifetime. Understanding the mechanisms long coherence lifetimes provides an avenue for rational design of materials capable of highly efficient charge and information transport.

The group recently constructed a three-state time-dependent model for studying coherence and performed real-time electron dynamics simulations of excited states of these complexes with frozen nuclei. This was done in order to isolate any purely electronic mechanisms underlying coherence. This protocol was then applied to four different related bimetallic Pt(II) complexes with varying Pt—Pt bond distances to investigate any correlation between those distances and the coherence lifetimes of those complexes.

Through this work we have shown that the three-state model for coherence is an appropriate representation of the two-state coherences exhibited by these complexes. Additionally, the time evolution of observable quantities including the excited state populations and transition dipole moments all feature the same oscillatory features characteristic of coherence. This work also shows a stark correlation between the Pt — Pt distance and the dephasing times of the four complexes simulated. This work is published in the Journal of Physical Chemistry A and can be found here.